Discussion of: Carry. by: Ralph Koijen, Toby Moskowitz, Lasse Pedersen, and Evert Vrugt. Kent Daniel. Columbia University, Graduate School of Business

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1 Discussion of: Carry by: Ralph Koijen, Toby Moskowitz, Lasse Pedersen, and Evert Vrugt Kent Daniel Columbia University, Graduate School of Business LSE Paul Woolley Center Annual Conference 8 June, 2012

2 Outline Defining Carry Carry Returns Empirical Findings Carry differences across commodities Carry Unwinds

3 Carry Everywhere The Carry Literature Interpreting Carry Futures Return Calculation Using a simple and (relatively) uniform carry measure, KMPV show that long-short carrys portfolio exhibit strong performance in four asset classes: 19 currencies. Global equity indices in 13 countries. Government bonds in 10 countries. 23 commodities. 6 metals; 6 energy; 8 agriculture; 3 livestock. The long-short portfolio weights assets in each class with a clever weighting scheme. In contrast to much of the currency carry literature.

4 Carry Literature The Carry Literature Interpreting Carry Futures Return Calculation There is a long literature documenting currency-carry, and forms of carry in other asset classes Currencies: Bilson (1981) Term Structure: Fama and Bliss (1987) Dividend Yields: Fama and French (1988) Commodities: Gorton, Hayashi, and Rouwenhorst (2012) However, the consistent performance of carry across asset-classes has not been recognized or illustrated as it is here.

5 Carry Literature The Carry Literature Interpreting Carry Futures Return Calculation There is a long literature documenting currency-carry, and forms of carry in other asset classes Currencies: Bilson (1981) Term Structure: Fama and Bliss (1987) Dividend Yields: Fama and French (1988) Commodities: Gorton, Hayashi, and Rouwenhorst (2012) However, the consistent performance of carry across asset-classes has not been recognized or illustrated as it is here.

6 Carry Literature The Carry Literature Interpreting Carry Futures Return Calculation There is a long literature documenting currency-carry, and forms of carry in other asset classes Currencies: Bilson (1981) Term Structure: Fama and Bliss (1987) Dividend Yields: Fama and French (1988) Commodities: Gorton, Hayashi, and Rouwenhorst (2012) However, the consistent performance of carry across asset-classes has not been recognized or illustrated as it is here.

7 Carry Literature The Carry Literature Interpreting Carry Futures Return Calculation There is a long literature documenting currency-carry, and forms of carry in other asset classes Currencies: Bilson (1981) Term Structure: Fama and Bliss (1987) Dividend Yields: Fama and French (1988) Commodities: Gorton, Hayashi, and Rouwenhorst (2012) However, the consistent performance of carry across asset-classes has not been recognized or illustrated as it is here.

8 Carry definition The Carry Literature Interpreting Carry Futures Return Calculation In words, carry is very simply defined as: the return that would be earned if the spot price didn t change. Consistent with this, the mathematical definition employed by KMPV is: C t = S t F t F t where S t is spot price and F t the one period forward. Depending on the asset class, the measure actually used varies somewhat.

9 Basic Currency Carry The Carry Literature Interpreting Carry Futures Return Calculation Graphically, currency carry is often illustrated as: Foreign Currency S t. e rf* S t+1 1/S t. e rf* 1/S t Domestic Currency And, by arbitrage, $1 (S t+1 /S t ). e rf*. e rf $1. e rf $1 F t = S t e (r f t r f t )

10 The basic idea The Carry Literature Interpreting Carry Futures Return Calculation The futures price thus reflects the interest rate differential: F t = S t e (r f t r f t ) That is, F t is always the future value of the spot, minus the carry. If it didn t there would be an arbitrage opportunity. However, suppose that the spot price doesn t change (or vary with the carry) then buying a future today (at F t ), and then taking delivery and selling at the spot (S t+1 = S t ) gives a cash-flow of: S t+1 F t = S t F t Normalizing by F t gives the KMPV carry measure: C t = S t F t F t

11 Equity Carry The Carry Literature Interpreting Carry Futures Return Calculation Very similar arguments apply to equities and bonds. If two equities pay continuously compounded dividends d i :. e d 1 Stock 1: S 1 t S 1 t+1 (S 1 t+1/s 1 t). e d 1 Stock 2:. e d 2 S 2 t S 2 t+1 (S 2 t+1/s 2 t). e d 2

12 Commodity Carry The Carry Literature Interpreting Carry Futures Return Calculation There is a rough equivalent for commodities: if the two commodities have storage costs expressed as continuous rates s i :. e -s 1 Cmdty 1: S 1 t $1 S 1 t+1 (S 1 t+1/s 1 t). e -s 1 Cmdty 2:. e -s 2 S 2 t S 2 t+1 (S 2 t+1/s 2 t). e -s 2 $1

13 Futures Return Calculation The Carry Literature Interpreting Carry Futures Return Calculation Since futures are zero investment contracts, the calculation of a futures return is a little ambiguous. One approach is to take into account the collateral X required to enter the futures contract. Then, the total payoff on the collateralized future contract is and the return is: Xe r f t + S t+1 F t R(X) = S t+1 F t + Xe r t f Xe r t f 1 As X changes the leverage on the forward contract changes For a fully collateralized futures (X = F t ): R(X) = S t+1 F t F t + (e r f t 1)

14 Futures Return Calculation The Carry Literature Interpreting Carry Futures Return Calculation The futures return, taking into account the collateral, is: This suggests two things: R(X) = S t+1 F t + Xe r t f Xe r t f 1 1 It might be important to include the risk-free rate of interest in cases where the returns are calculated using futures. 2 Should contracts be scaled by volatility before rank-weighting? Volatility weighting across asset classes seemed sensible and worked well ex-post. Why not do it within asset classes (and across time) as well?

15 of Empirical Findings Commodity Carry Static vs. Dynamic KMPV s empirical findings are that: In each asset class, the long-short carry portfolio yields high returns and high Sharpe-ratio Sharpe-ratios run between 0.5 and 0.9 in asset classes. Combined/Global carry portfolio SR = 1.41 asset-class carry portfolio returns are relatively uncorrelated The results are consisten for Current Carry, and for 1-year average carry (Carry1-12). Standard risk-adjustment techniques don t eliminate the carry premium. Carry predicts returns out about 1 year. Both static and dynamic components of carry are important. Diversified carry trade seems exposed to business cycle risk.

16 Commodity Carry Static vs. Dynamic Commodity Carry KMPV run a set of panel regressions: r i t+1 = ai + b t + cc i t + ɛ i t+1 One particularly intriguing finding is that c << 1 for commodities: high s(δ) yields forecast strong future p: Panel A: Current Carry Cumulative returns Cumulative carry Equities 15 Commodities Fixed income Currencies

17 Wheat Futures Commodity Carry Static vs. Dynamic 740 Wheat Futures Price -- 5 June Price (cents/bushel) Jul 2012 Oct 2012 Jan 2013 Apr 2013 Jul 2013 Oct 2013 Contract Maturity Jan 2014 Apr 2014 Jul 2014

18 Soybeans Futures Commodity Carry Static vs. Dynamic 1350 Soy Futures Price -- 5 June Price (cents/bushel) Jul 2012 Nov 2012 Mar 2013 Jul 2013 Nov 2013 Mar 2014 Contract Maturity Jul 2014 Nov 2014 Mar 2015 Jul 2015 Nov 2015

19 Corn Futures Commodity Carry Static vs. Dynamic 570 Corn Futures Price -- 5 June 2012 Price (cents/bushel) Oct 2012 Feb 2013 Jun 2013 Oct 2013 Feb 2014 Contract Maturity Jun 2014 Oct 2014 Feb 2015 Jun 2015 Oct 2015

20 Commodity Carry Static vs. Dynamic Agricultural Futures-Price Curves CME Commodity Prices -- 5 June 2012 corn wheat soy (X 1/2) Price (cents/bushel) Oct 2012 Feb 2013 Jun 2013 Oct 2013 Feb 2014 Contract Maturity Jun 2014 Oct 2014 Feb 2015 Jun 2015 Oct 2015

21 Carry for Agricultural Futures Commodity Carry Static vs. Dynamic Annualized Commodity Carry (as of 5 June 2012) corn wheat soy Carry (/year) Jul 2012 Nov 2012 Mar 2013 Jul 2013 Nov 2013 Mar 2014 Jul 2014 Nov 2014 Contract Maturity Date Mar 2015 Jul 2015

22 Carry for Metals Futures Commodity Carry Static vs. Dynamic Annualized Commodity Carry (as of 5 June 2012) gold silver copper Carry (/year) Contract Maturity Date

23 Carry for Metals Futures Commodity Carry Static vs. Dynamic Annualized Commodity Carry (as of 5 June 2012) gold silver copper 0.01 Carry (/year) Contract Maturity Date

24 Commodity Carry Static vs. Dynamic Metals Futures - Futures Curves gold silver copper CME Commodity Prices -- 5 June 2012 Normalized Price Contract Maturity

25 Commodity Carry Static vs. Dynamic 4.3 Decomposing Carry Trade Returns Into Static and Dynamic Components Static vs. Dynamic Components of Carry The average return of the carry trade depends on two sources of exposure: (i)a passive return component due to the average carry trade portfolio being long (short) securities The analysis of static vs. dydnamic components of carry finds that the fraction of the carry return that can be attributed to the passive component of the strategy runs from 25% (global equities) to 67% (commodities). that have high (low) unconditional returns, and (ii) a dynamic return component that captures how strongly variation in carry predicts returns. More formally, we decompose carry trade returns into its passive and dynamic components as follows (recall that w i t is the portfolio weight of security i): carry trade E(rt+1 ) = E( i w i tr i t+1) = E(wt i )E(ri t+1 ) + E [( wt i E(wi t ))( rt+1 i E(ri t+1 ))]. (20) i i }{{}}{{} E(r passive ) E(r dynamic ) However, the earlier data here starts in the mid 1980 s. Here, E(w i t)istheportfolio s passiveexposure toasseti, whilethe dynamicexposure w i t E(wi t )iszeroonaverageovertime,representingatimingstrategyintheassetthat Many data series start in the mid- to late goes long and short according to the asset s carry. Thus the analysis seems biased towards the finding of large static premia. 23

26 Carry Skewness Crash Risk Consumption Risk Of course, one of the goals of this paper is to determine the underlying economic mechanism that is responsible for the premium earned by carry strategies. For currencies, a set of explanations relate to the risk associated with currency-crash risk: e.g., Farhi and Gabaix (2008), Brunnermeier, Nagel, and Pedersen (2008). What is striking here is that, apart from currencies, there is little negative skewness associated with non-currency carry strategies. This is particularly true for the regional strategies KMPV examine. Thus, crash risk doesn t seems to be driving carry premia.

27 Common Factor Crash Risk Consumption Risk Another set of explanations rely on the exposure of carry trades to some common factor. E.g., Lustig and Verdelhan (2007) argue that the currency carry trade is exposed to aggregate consumption growth risk. Several pieces of the the evidence here seem inconsistent with this explanation: carry trades close to uncorrelated across asset classes. High Sharpe ratio for diversified carry strategy. (SR= 1.41.) However, the fact that carry trades all tend to fall during downturns is perhaps consistent with this hypothesis. This is perhaps related to the (casual) fact that markets seem to crash sequentially in financial crises sometimes with long lags between crashes.

28 Carry Drawdowns Crash Risk Consumption Risk 0 Equities 0 Fixed income EQ Drawdowns GCF Drawdowns Currencies 0 Commodities Figure 7: Draw-down Dynamics Per Asset Class. The figure shows the maximum draw-down dynamics of Kenthe Daniel global Columbia carry1-12 GSB strategy. Carry LSE-Woolley We Center define Discussion the draw down as:

29 References I Crash Risk Consumption Risk Bilson, John F.O., 1981, The speculative efficiency hypothesis, Journal of Business 54, Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen, 2008, Carry trades and currency crashes, NBER Macroeconomics Annual. Fama, Eugene F., and Robert R. Bliss, 1987, The information in long-maturity forward rates, The American Economic Review 77, Fama, Eugene F., and Kenneth R. French, 1988, Dividend yields and expected stock returns, Journal of Financial Economics 22, Farhi, Emmanuel, and Xavier Gabaix, 2008, Rare disasters and exchange rates, NBER Working Paper. Gorton, Gary B., Fumio Hayashi, and K. Geert Rouwenhorst, 2012, The fundamentals of commodity futures returns, Review of Finance, forthcoming. Lustig, Hanno N., and Adrien Verdelhan, 2007, The cross section of foreign currency risk premia and consumption growth risk, The American Economic Review 97,